
Then from the branching ratios and the values of \(\alpha \)  for each channel, their \(|G_E|\)  and \(|G_M|\)  can be computed as shown in Table REF .
As described in Ref. [1]}, the sign difference of \(\alpha \)  between \(\Sigma ^0\bar{\Sigma }^0\)  and \(\Lambda \bar{\Lambda }\)  can be explained by using a SU(3) symmetry breaking model [2]}.
In Ref. [2]}, they provide all amplitudes listed in Table  REF , where \(G_0\)  is related to the three gluons interaction within SU(3) symmetry, \(D_e\)  and \(F_e\)  for the EM breaking effects, \(D_m\)  and \(F_m\)  describe the mass difference breaking effects, \(\phi \)  is relative phase between strong interaction and EM interaction, \(R\)  is the ratio between \(gg\gamma \)  and \(ggg\)  contributions.
By following the method of Ref. [1]}, we can decompose the electric and magnetic amplitudes as the different parts, respectively.
At last for electric and magnetic amplitudes, we can solve them independently, the results are shown in Table REF .
From these solutions, we can find that the \(g_0\)  of electric amplitudes is even smaller than that of other symmetry breaking terms, while \(g_0\)  is dominant in the magnetic amplitudes.
Of course such parameters are not proper, especially for the electric amplitudes.
However, in Ref. [2]}, this model is able to explain the branching ratios since most channels are dominated by the magnetic amplitudes.
In Ref. [1]}, they use this model explain the \(\alpha \)  for the \(\Sigma ^0\bar{\Sigma }^0\)  and \(\Lambda \bar{\Lambda }\) , but once all octets baryon channels are considered it is not so reasonable to explain the values of \(\alpha \)  which need electric and magnetic amplitudes both well described.
Thus, beside the SU(3) breaking effect mentioned above, other mechanisms are needed to solve this problem.
For example, for the \(\Sigma \)  the total spin and isospin of light quark pair are both 1, i.e., so called “bad diquark” [7]}, [8]}, while for the \(\Lambda \)  the [ud] quark pair has both spin and isospin to be 0, i.e., so called “good diquark”.
It may be a reason causing the angular distribution difference for the case of \(\Sigma \bar{\Sigma }\)  from others.
The hadronic loops may be another possible mechanism.
The study of these possible mechanisms are beyond the scope of this paper and should be explored in the future.
An important point is : although the detailed production mechanisms may be different to cause the difference of angular distributions, the deduced small effective radii for their production from vector charmonium annihilation are nearly the same and lead to the S-wave dominant final states for both cases.
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